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Abstract: Transport times for a chaotic system are highly sensitive to initial conditions and parameter values. In an area preserving twist map, Mather sets (including KAM curves) imply a high degree of "ordered chaos," and present barriers to transport. Transport for such maps is extremely slow due to the ''stickiness" of island chains.
I will present a technique to find rough orbits (epsilon-chains) that achieve a desired transport rapidly and which can be stabilized with small parameter perturbations. The strategy is to build the epsilon-chain from segments of a long orbit. The Mather sets imply that long orbits must have recurrences in regions where faster orbits must also pass. Using the recurrence points as switching regions, we concatenate a rough orbit by choosing just the segments of the long orbit which we ''need", but with large errors. If a local hyperbolicity condition is also satisfied, then a nearby shadow orbit may be constructed with significantly smaller errors and fast transport. We apply this technique to the standard map and then to the restricted three body problem as a model to find fast and low energy transport to the Moon.